We note that the approach becomes computationally expensive when the spatial dimension increases. Indeed, it becomes impracticable when the data are collected for 2D or 3D space. A large system parameter space imposes additional challenges. However, we know that the dynamics often lie in a low-dimensional manifold. Therefore, in our future work, we aim to utilize the concept of low-dimensional embedding to make learning computationally more efficient.
Furthermore, we learn a dynamic model as a black-box neural network. Hence, interpretability and generalizability remain opaque. In the future, it could be interesting to combine or use the de-noised data with sparse or symbolic regression, as, e.g., in [1]}, [2]}, [3]} to obtain an analytic expression for a (partial) differential equations explaining the data.
